02-03ChapGere.0003

02-03ChapGere.0003 - 108 A-PDF Axially Loaded : Purchase...

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108 CHAPTER 2 Axially Loaded Members Solution 2.5-5 Bar with nonuniform temperature change At distance x : R EMOVE THE SUPPORT AT END B OF THE BAR : Consider an element dx at a distance x from end A . ¢ T 5 ¢ T B ¢ x 3 L 3 d d 5 Elongation of element dx d 5 elongation of bar C OMPRESSIVE FORCE P REQUIRED TO SHORTEN THE BAR BY THE AMOUNT d C OMPRESSIVE STRESS IN THE BAR s c 5 P A 5 E a ( ¢ T B ) 4 Ê P 5 EA d L 5 1 4 EA a ( ¢ T B ) d 5 # L 0 d d 5 # L 0 a ( ¢ T B ) ¢ x 3 L 3 dx 5 1 4 a ( ¢ T B ) L d d 5 a ( ¢ T ) dx 5 a ( ¢ T B ) ¢ x 3 L 3 dx L A T T B B x 0 L AB x dx Problem 2.5-6 A plastic bar ACB having two different solid circular cross sections is held between rigid supports as shown in the figure. The diameters in the left- and right-hand parts are 50 mm and 75 mm, respectively. The corresponding lengths are 225 mm and 300 mm. Also, the modulus of elasticity E is 6.0 GPa, and the coefficient of thermal expansion a is 100 3 10 2 6 /°C. The bar is subjected to a uniform temperature increase of 30°C.
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